A note on strict feasibility and solvability for pseudomonotone equilibrium problems

Volume 9, Issue 11, pp 5894--5899 http://dx.doi.org/10.22436/jnsa.009.11.16

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Authors

Rabian Wangkeeree - Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand. Pakkapon Preechasilp - Program in Mathematics, Faculty of Education, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

Abstract

The aim of this note is to establish the characterization of nonemptiness and boundedness of the solution set of equilibrium problem with stably pseudomonotone mappings. Our result extends and improves recent results in the literature for monotone equilibrium problems.

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Keywords

• Equilibrium problem
• strict feasibility
• stably pseudomonotone mapping.

MSC

•  49J40

References

• [1] S. Adly, E. Ernst, M. Théra, Well-positioned closed convex sets and well-positioned closed convex functions, J. Global Optim., 29 (2004), 337--351


• [2] M. Bianchi, R. Pini, A note on equilibrium problems with properly quasimonotone bifunctions, J. Global Optim., 20 (2001), 67--76


• [3] M. Bianchi, R. Pini, Coercivity conditions for equilibrium problems, J. Optim. Theory Appl., 124 (2005), 79--92


• [4] M. Bianchi, S. Schaible, Generalized monotone bifunctions and equilibrium problems, J. Optim. Theory Appl., 90 (1996), 31--43


• [5] E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1993), 123--145


• [6] K. Fan, Some properties of convex sets related to fixed point theorems, Math. Ann., 266 (1984), 519--537


• [7] Y.-P. Fang, N.-J. Huang, Equivalence of equilibrium problems and least element problem, J. Optim. Theory Appl., 132 (2007), 411--422


• [8] Y. R. He, A relationship between pseudomonotone and monotone mappings, Appl. Math. Lett., 17 (2004), 459--461


• [9] Y. R. He, X. Z. Mao, M. Zhou, Strict feasibility of variational inequalities in reflexive Banach spaces, Acta Math. Sin. (Engl. Ser.), 23 (2007), 563--570


• [10] Y. R. He, K. F. Ng, Strict feasibility of generalized complementarity problems, J. Aust. Math. Soc., 81 (2006), 15--20


• [11] R. Hu, Y.-P. Fang, A characterization of nonemptiness and boundedness of the solution sets for equilibrium problems, Positivity, 17 (2013), 431--441


• [12] R. Wangkeeree, P. Preechasilp, Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces, J. Global Optim., 57 (2013), 1447--1464